In this thesis block circulant boundary meshes are introduced to 3-dimensional electromagnetic scattering problem to overcome excessive storage requirement of hybrid finite element-boundary element method. In addition, edge elements are incorporated for this vectorial hybrid method. This boundary mesh makes use of axi-symmetry to produce block circulant boundary element matrices, and results in up to 64-fold reduction in matrix storage. To demonstrate its efficiency this hybrid scheme is applied to a time-harmonic electromagnetic scattering from a double-layered dielectric sphere.